Prove that lim

Problem: 

If
\begin{equation} \lim_{x\to a}\,f(x)=L \end{equation}
and
\begin{equation} \lim_{x\to a}\,g(x)=K \end{equation}
then prove that
\begin{equation} \lim_{x\to a}\,f(x)\,g(x)=LK. \end{equation}

Answer: 

It is true that \begin{equation}\lim_{x\to a}\,f(x)\,g(x)=LK.\end{equation}